Trainable quantum spectral models with an intermediate parameterized mixer (ε ≈ 0.5) outperform standard variational quantum circuits for PDEs by learning in spectral representation, with HHL-inspired architectures showing fastest convergence.
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End-to-end QSP-based quantum circuits solve linear PDEs on IBM hardware with tunable error and handle non-homogeneous Dirichlet boundaries for a plasma Poisson problem.
PDEs are solved by formulating discretized systems as generalized eigenvalue problems and using annealing to optimize the generalized Rayleigh quotient iteratively for eigenvectors.
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Trainable Quantum Spectral Models for Partial Differential Equations
Trainable quantum spectral models with an intermediate parameterized mixer (ε ≈ 0.5) outperform standard variational quantum circuits for PDEs by learning in spectral representation, with HHL-inspired architectures showing fastest convergence.
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Quantum Signal Processing for Linear PDEs: Circuit Design and Experimental Validation
End-to-end QSP-based quantum circuits solve linear PDEs on IBM hardware with tunable error and handle non-homogeneous Dirichlet boundaries for a plasma Poisson problem.
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Annealing-based approach to solving partial differential equations
PDEs are solved by formulating discretized systems as generalized eigenvalue problems and using annealing to optimize the generalized Rayleigh quotient iteratively for eigenvectors.